Problem: Simplify the following expression: $\sqrt{2}+\sqrt{50}-\sqrt{32}$
Explanation: First, try to factor any perfect squares out of the radicals. $= \sqrt{2}+\sqrt{50}-\sqrt{32}$ $= \sqrt{2}+\sqrt{25 \cdot 2}-\sqrt{16 \cdot 2}$ Separate the radicals and simplify. $= \sqrt{2}+\sqrt{25} \cdot \sqrt{2}-\sqrt{16} \cdot \sqrt{2}$ $= \sqrt{2}+5\sqrt{2}-4\sqrt{2}$ Finally, simplify by combining the terms. $= ( 1 + 5 - 4 )\sqrt{2} = 2\sqrt{2}$